When using finely divided solids in industrial and scientific applications, it is often necessary to determine the distribution of the sizes of particles making up the sample. It may be critical, for example, that a catalyst be made up of particles at least a certain percentage of which by weight are smaller than a certain diameter. A typical manner in which particle size information is presented is the particle size distribution curve, which plots percent finer against particle size.
One widely used technique for determining particle size data uses Stokes' Law of sedimentation, which provides that at a given time after sedimentation of the sample suspended in a liquid has begun, particles larger than a given size will have fallen below a certain distance from the surface of the suspension. It follows that the percent of particles finer than the given size can be determined from the concentration of all particles at the certain distance. The transmission of x-rays through the suspension is a function only of the weight concentration of suspended solids, and therefore has provided the most convenient and accurate way to measure concentration in carrying out the sedimentation technique. Devices have been made using other electromagnetic radiation, such as visible light.
Significant economy in the time required for such an analysis was realized with the concept of continuously moving the sample cell and radiation source relative to one another during sedimentation while moving a pen plotting the particle size axis of the particle size distribution curve in a coordinated fashion to at all times satisfy Stokes' Law. This concept was disclosed in the early work of Muta, U.S. Pat. No. 3,315,066 and of Kalshoven, British Pat. No. 1,158,338. Subsequent improvements disclosed in U.S. Pat. Nos. 3,449,567 and 3,621,243 to Olivier and Hickin led to successful commercial embodiments, among them the Sedigraph 5000 series of instruments manufactured by Micromeritics Instrument Corporation. Detailed theoretical descriptions of the implementation of Stokes' Law in scanning x-ray particle size analyzers may be found in the patents listed above.
The length of time required for an analysis providing data for small particle sizes, e.g., down to 0.1 micron, has remained a problem with such instruments. In prior instruments, the cell must be moved very slowly in order to position it in a timely manner to record accurate data for the continuum of cell positions near the top of the cell. Run times of many hours, depending upon the nature of the sample and the suspending liquid, are the result. Furthermore, the distribution curve must be generated over the same length of time, even if an operator needs only a lower level of precision.
Sample cells for use with sedimentation particle size analyzers are designed to attempt to provide minimum distortion of the x-ray beam by the cell, to provide a bubble-free x-ray path, and to provide maximum dispersion of the sample in the liquid. A problem experienced with current analyzers has been difficulty in obtaining uniform dispersion of sample particles in the suspension prior to the beginning of sedimentation. Sample cells are typically connected via tubing to a mixing chamber, from which the suspension is pumped to the cell. Recirculation of the suspension through the cell and the mixing chamber has been relied upon to maintain a uniform suspension. However, because of interior cell geometry and the location of ports to which the tubing is attached, it has been found that areas of the cell often are not adequately swept by the flow of fluid, and therefore experience some premature settling of larger particles. This can result in an analysis indicating that the sample is finer than it is in fact.
Another problem has been a lack of precise reproducibility of the results obtained for the same sample, particularly from machine to machine of the same type. It is now suspected that the input and output tubing connected to the cell provides horizontal settling channels in which a density gradient can be created. The lighter portion of the suspension at the top of the tubing would have a tendency to rise, and could rise to the top of the cell itself. The presence of less dense material at the top of the cell not resulting from sedimentation in the cell itself would skew the observations taken in that region.
This problem is not as significant in cells which have both inlet and outlet at the top of the cell. However, it is important to have a port at the bottom of the cell to provide better flushing action for the removal of sedimentation deposits.
The introduction of closed-top cells facilitated accurate analysis of very small particles by eliminating the meniscus at the top of the suspension volume and thereby allowing precise determination of the sedimentation height. However, the closed cell created a greater likelihood that bubbles rising to the top of the cell would become trapped in the path of the x-ray beam. Such bubbles falsely reduced the apparent density of the suspension measured by the x-rays, and were quite capable of rendering an analysis useless. As they often were not detected except in the form of obviously flawed output, such bubbles often resulted in the waste of many hours required to re-run the sample.
In prior x-ray particle size analyzers, it is important that the x-ray path through the cell be uniform along the entire scanned height of the cell. The measured transmission of x-rays during a run is used to calculate "percent finer" according to the following equation: ##EQU1## where I.sub.o is the transmittance through the cell containing only the suspending fluid, I.sub.100 is the transmittance through the cell containing the sample fully suspended before sedimentation, and I.sub.x is the measured transmittance at a height and time during a run. Calibration of the cell requires a determination of I.sub.o and I.sub.100. If the effect of the cell on the x-rays along the height of the cell is not uniform, I.sub.o and I.sub.100 will not have a constant value for all measuring heights.
In prior analysers, the construction of the cell has been made to fine tolerances in order to attempt to provide clear windows mounted in exactly parallel relationship to one another. These attempts have not been entirely successful. Furthermore, the cell windows can become dirty in a non-uniform manner, adding to the problem. Some prior analyzers have made a single measurement of I.sub.o and of I.sub.100 at a selected cell height, and assumed that the cell is sufficiently uniform. Another technique has been to measure I.sub.o and I.sub.100 at several heights and to accept the average of these measurements as representative of the cell for all calculations of percent finer. All such techniques result in somewhat inaccurate particle size results if there is a significant difference in cell transmittance characteristics at different heights along the cell.
Thus, there has been a need in the art for an x-ray particle size analyzer capable of faster analysis, capable of highly uniform dispersion of the sample prior to sedimentation, not affected by sedimentation in tubing, capable of detecting and eliminating bubbles before the start of a run, and capable of compensating in a meaningful way for nonuniformities in x-ray transmission by the cell.